The $t/k$-Diagnosability of Star Graph Networks

Zhou, Shuming; Lin, Limei; Xu, Li; Wang, Dajin

doi:10.1109/tc.2013.228

Cited by 62 publications

(1 citation statement)

References 37 publications

(52 reference statements)

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“…For n ⩾ 4 and n ⩾ k ⩾ 1, it is proved by Somani et al [2] that the hypercube Q n is [(k + 1)n − (k+1)(k+2) 2 + 1]/k-diagnosable. The t/k-diagnosability of several networks under the PMC model has been determined, including hypercubes [2], star graphs [2,5], mesh-based systems [2], and bijective connection (BC) networks [6,7]. Recently, by utilizing the properties of the 0-test subgraph under the PMC model, Lin et al [8] studied the t/k-diagnosability of regular graphs under the PMC model.…”

Section: Introductionmentioning

confidence: 99%

t/k-Diagnosability of Regular Networks under the Comparison Model

Liang,

Xiao,

Lin

et al. 2024

Sensors

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As multiprocessor systems continue to grow in processor scale, the incidence of faults also increases. As a result, fault diagnosis is becoming a key mechanism for maintaining the normal operation of multiprocessor systems. To explore more effective diagnostic methods, Somani et al. introduced a generalized pessimistic diagnostic strategy, named t/k-diagnosis, in which all faulty nodes are isolated in a set of nodes and at most k fault-free nodes are misdiagnosed, provided that the quantity of faults is limited by t. By imposing certain conditions or restrictions, the t/k-diagnosability of some regular networks under the Preparata, Metze, and Chien (PMC) model has been determined. However, the t/k-diagnosability of many networks under the comparison model remains unidentified. In this paper, we provide new insights into the study of t/k-diagnosability under the comparison model. After introducing some new notions, such as the 0-test unit, 0-test set and 0-test subgraph, under the comparison model, we study the relationship in a system G between the 0-test subgraphs and the components of G−F, where F is the set of faulty nodes, and we obtain some important correlation properties. Based on these results, we study t/k-diagnosability under the comparison model. As a result, the t/k-diagnosability of some regular interconnection networks can be efficiently determined.

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Section: Introductionmentioning

confidence: 99%

t/k-Diagnosability of Regular Networks under the Comparison Model

Liang,

Xiao,

Lin

et al. 2024

Sensors

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Local diagnosability under the PMC model with application to matching composition networks

Jiang

Wei-di

Gui

et al. 2019

Concurrency and Computation

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Matching composition network is a family of interconnection networks, including the BC network and the hyper Petersen network, etc. In this paper, we prove that the local diagnosability of an MCN can be obtained by adding one to that of the component with some structural restrictions. Additionally, we obtain a sufficient condition for verifying that an MCN with fault-free edges (faulty edges, respectively) has strong local diagnostic properties. By applying these results, the BC network BC n and the hyper Petersen network HP n are n l -diagnosable at each node belonging to them, for n ⩾ 3. These interconnection networks with fault-free edges (faulty edges, respectively) possess the strong local diagnosability property. KEYWORDSfault diagnosis, local diagnosability, matching composition network, PMC model INTRODUCTIONWith the scale of the high-performance parallel computer systems growing larger, the system architecture has become more and more complex.However, the complex architecture of these multiprocessor systems has a negative impact on the reliability of such systems. Due to the influence of many factors such as production process, system integration, and system operating environment, the more processors and communication links, the higher the probability of failure. In some cases, some of the processors fail, which may cause the entire system to lose its ability to work.Consequently, promptly locating and replacing the faulty processors are absolutely essential for guaranteeing the reliability of a multiprocessor system.During the development of system diagnosis, researchers proposed several diagnostic models. The PMC model is undoubtedly one of the most widely used models. 1 There are two different diagnostic strategies depending on whether all faulty nodes in the system are identified one or more times under the PMC model. One is one-step diagnostic strategy and the other is sequential diagnostic strategy. 1 These two diagnostic strategies are both based on the same assumption that all neighbor processors of any one of the processors in the system may fail simultaneously. Therefore, the number of faulty processors that these diagnostic strategies can identify must be limited by the minimum number of neighbors for any one of the processors in the system. To overcome this restriction and increase the system's fault diagnosis capabilities, the researchers proposed different diagnostic strategies and made many attempts. The t/k-diagnosability 2 approach increases the diagnostic capabilities of the system by allowing at most k processors to be diagnosed incorrectly. Obviously, the shortcoming of the t/k-diagnostic strategy is that it may diagnose a fault-free node as a faulty node. Araki et al 3 proposed the (t, k)-diagnosis by introducing a new parameter k, which extended the application of sequential diagnostic strategies and revealed the correlation between one-step diagnosis and generalized sequential diagnosis. However, the choice of the parameter k is a challenge that affects diagnostic efficiency. Provi...

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A Comparison Diagnosis Algorithm for Conditional Fault Local Diagnosis of Multiprocessor Systems

Lin

Hsu

et al. 2022

Communications in Computer and Information Science

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The $t/k$-Diagnosability of Star Graph Networks

Cited by 62 publications

References 37 publications

t/k-Diagnosability of Regular Networks under the Comparison Model

t/k-Diagnosability of Regular Networks under the Comparison Model

Local diagnosability under the PMC model with application to matching composition networks

A Comparison Diagnosis Algorithm for Conditional Fault Local Diagnosis of Multiprocessor Systems

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